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Introduction to Numerical Linear Algebra and Optimisation

Introduction to Numerical Linear Algebra and Optimisation

$89.99 (X)

textbook

Part of Cambridge Texts in Applied Mathematics

  • Date Published: August 1989
  • availability: Available
  • format: Paperback
  • isbn: 9780521339841

$ 89.99 (X)
Paperback

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  • Based on courses taught to advanced undergraduate students, this book offers a broad introduction to the methods of numerical linear algebra and optimization. The prerequisites are familiarity with the basic properties of matrices, finite-dimensional vector spaces and advanced calculus, and some exposure to fundamental notions from functional analysis. The book is divided into two parts. The first part deals with numerical linear algebra (numerical analysis of matrices, direct and indirect methods for solving linear systems, calculation of eigenvalues and eigenvectors) and the second, optimizations (general algorithms, linear and nonlinear programming). Summaries of basic mathematics are provided, proof of theorems are complete yet kept as simple as possible, applications from physics and mechanics are discussed, a great many exercises are included, and there is a useful guide to further reading.

    Reviews & endorsements

    "...a very thorough introduction to the common numerical methods used in linear algebra and optimization theory. The text is well written..." Choice

    "...gives exact and, in most cases, exceedingly elegant proofs of the existence and convergence theorems underlying the commonly used algorithms and clearly presents the necessary mathematical background beyond that of a general requirement of elementary linear algebra and advanced calculus." Computing Reviews

    "...certainly a valuable and welcome addition to the literature. It is a joy to read for those who have a solid background in mathematics." Bulletin of the International Linear Algebra Society

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    Product details

    • Date Published: August 1989
    • format: Paperback
    • isbn: 9780521339841
    • length: 452 pages
    • dimensions: 225 x 150 x 26 mm
    • weight: 0.555kg
    • availability: Available
  • Table of Contents

    Preface
    Part I. Numerical Linear Algebra:
    1. A summary of results on matrices
    2. General results in the numerical analysis of matrices
    3. Sources of problems in the numerical analysis of matrices
    4. Direct methods for the solution of linear systems
    5. Iterative methods for the solution of linear systems
    6. Methods for the calculation of eigenvalues and eigenvectors
    Part II. Optimisation:
    7. A review of differential calculus. Some applications
    8. General results on optimisation. Some algorithms
    9. Introduction to non-linear programming
    10. Linear programming
    Bibliography and comments
    Main notations used
    Index.

  • Author

    Philippe G. Ciarlet

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